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                  <h4>nlinvp</h4>Non-Linear inverse problem
                  <br><small>Last modified: 09-Sep-2010 17:49:55</small>

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                  <a href="http://guillaumemaze.googlecode.com/svn/trunk/matlab/codes/stats/nlinvp.m">Download here</a>
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                  <br>% nlinvp  Non-Linear inverse problem<br>%<br>% [Xs, Cs, FXs, FX0] = nlinvp(X0,C0,F,CT,F0,[OPTIONS])<br>% <br>% Solve a non-linear inverse problem.<br>%<br>% Given f a set of constraints to be applied at points X<br>% F is the matrix of partial derivatives of f with respect to X:<br>%	F(t,k) = d f(t) / d X(k)<br>% Because the problem is non-linear, any X(k) can be found in F(t,k)<br>%<br>% With:	<br>% 	NC the Number of constraints and<br>% 	NU the Number of unknowns to be estimated,<br>%<br>% INPUTS:<br>%	X0: A priori unknowns estimates<br>%		size(X0) = NU x 1<br>%	C0: A priori error covariance matrix of unknowns estimates<br>%		size(C0) = NU x NU<br>%	F: Constraints matrix<br>%		size(F) = NC x NU<br>% 	CT: A priori error covariance matrix on constraints<br>%		size(CT) = NC x NC<br>% 	F0: a priori constraints estimate -> f(X0)<br>%		size(F0) = NC x 1<br>%<br>% OUTPUTS:<br>% 	Xs: unknowns estimates<br>%		size(Xs) = NU x 1	<br>% 	Cs: error covariance matrix of unknowns estimates<br>%		size(Cs) = NU x NU<br>% 	FXs = F*Xs-F0: A posteriori constraints residuals<br>%		size(FXs) = NC x 1<br>% 	FX0 = F*X0-F0 : A priori constraints residuals<br>%		size(FX0) = NC x 1<br>%<br>% Ref: <br>%	A. Tarantola and B. Valette. Generalized nonlinear inverse problems <br>%		solved using the least squares criterion. <br>%		Rev. Geophys. Space Phys, 20(2):219–232, 1982.<br>% 	H. Mercier. Determining the general circulation of the ocean: A <br>%		nonlinear inverse problem. J. Geophys. Res., 91(C4):5103–5109, 1986.<br>%		http://dx.doi.org/10.1029/JC091iC04p05103<br>%<br>% See Also:<br>%	linvp<br>%<br>% Created: 2010-09-09.<br>% All rights reserved.
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                  Last update: 2011 March 04, 17:46<br>
                  Created by Guillaume Maze<br>
                  More informations at: <a href="http://codes.guillaumemaze.org/matlab">codes.guillaumemaze.org/matlab</a><br>
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